Select all of the true statements. Multi-select Choices: (A)1 * 10^-2 is 50 times as much as 2 * 10^-4. (B)8 * 10^2 is 0.02 times as much as 4 * 10^4. (C)3 * 10^-3 is 6 times as much as 5 * 10^-2. (D)8 * 10^9 is 2,000 times as much as 4 * 10^6.

Check (A): To check (A), compare 1 * 10^-2 and 2 * 10^-4. Calculate 50 times 2 * 10^-4 to see if it equals 1 * 10^-2. 50 * (2 * 10^-4) = 100 * 10^-4 = 1 * 10^-2. So, (A) is true.Check (B): For (B), compare 8 * 10^2 and 4 * 10^4. Calculate 0.02 times 4 * 10^4 to see if it equals 8 * 10^2. 0.02 * (4 * 10^4) = 0.08 * 10^4 = 8 * 10^2. So, (B) is true.Check (C): To check (C), compare 3 * 10^-3 and 5 * 10^-2. Calculate 6 times 5 * 10^-2 to see if it equals 3 * 10^-3. 6 * (5 * 10^-2) = 30 * 10^-2. This does not equal 3 * 10^-3, so (C) is false.Check (D): For (D), compare 8 * 10^9 and 4 * 10^6. Calculate 2,000 times 4 * 10^6 to see if it equals 8 * 10^9. 2,000 * (4 * 10^6) = 8,000 * 10^6 = 8 * 10^9. So, (D) is true.

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Select all of the true statements. $\newline$ Multi-select Choices: $\newline$ (A) $1 \times 10^{-2}$ is $50$ times as much as $2 \times 10^{-4}$ . $\newline$ (B) $8 \times 10^{2}$ is $0.02$ times as much as $4 \times 10^{4}$ . $\newline$ (C) $3 \times 10^{-3}$ is $6$ times as much as $5 \times 10^{-2}$ . $\newline$ (D) $8 \times 10^{9}$ is $50$ $0$ times as much as $50$ $1$ .

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Select all of the true statements.

\newline

Multi-select Choices:

\newline

(A)

1 \times 10^{-2}

50

times as much as

2 \times 10^{-4}

\newline

(B)

8 \times 10^{2}

0.02

times as much as

4 \times 10^{4}

\newline

(C)

3 \times 10^{-3}

6

times as much as

5 \times 10^{-2}

\newline

(D)

8 \times 10^{9}

50

0

times as much as

50

1

Check (A): To check (A), compare $1 \times 10^{-2}$ and $2 \times 10^{-4}$ . Calculate $50$ times $2 \times 10^{-4}$ to see if it equals $1 \times 10^{-2}$ . $\newline$ $50 \times (2 \times 10^{-4}) = 100 \times 10^{-4} = 1 \times 10^{-2}$ . $\newline$ So, (A) is true.
Check (B): For (B), compare $8 \times 10^2$ and $4 \times 10^4$ . Calculate $0.02 \times 4 \times 10^4$ to see if it equals $8 \times 10^2$ . $\newline$ $0.02 \times (4 \times 10^4) = 0.08 \times 10^4 = 8 \times 10^2$ . $\newline$ So, (B) is true.
Check (C): To check (C), compare $3 \times 10^{-3}$ and $5 \times 10^{-2}$ . Calculate $6$ times $5 \times 10^{-2}$ to see if it equals $3 \times 10^{-3}$ . $\newline$ $6 \times (5 \times 10^{-2}) = 30 \times 10^{-2}$ . $\newline$ This does not equal $3 \times 10^{-3}$ , so (C) is false.
Check (D): For (D), compare $8 \times 10^9$ and $4 \times 10^6$ . Calculate $2,000 \times 4 \times 10^6$ to see if it equals $8 \times 10^9$ . $\newline$ $2,000 \times (4 \times 10^6) = 8,000 \times 10^6 = 8 \times 10^9$ . $\newline$ So, (D) is true.